Oddly missing sign on hotel (3)
I believe the answer is:
inn
'hotel' is the definition.
(inn is a kind of hotel)
'oddly missing sign on' is the wordplay.
'oddly missing' indicates alternate letters (letters in odd-numbered positions removed).
'sign'+'on'='signon'
The alternating letters of 'signon' are 'INN'.
(Other definitions for inn that I've seen before include "bar" , "watering hole" , "place to stay" , "Pub with lodging" , "Small hotel or country pub" .)